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Journal of Applied Mathematics
Volume 2012, Article ID 973781, 15 pages
http://dx.doi.org/10.1155/2012/973781
Research Article

Newton Method to Recover the Phase Accumulated during MRI Data Acquisition

Department of Mathematics, Konkuk University, Seoul 143-701, Republic of Korea

Received 29 October 2012; Accepted 28 November 2012

Academic Editor: Changbum Chun

Copyright © 2012 Oh-In Kwon and Chunjae Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Joy, G. Scott, and M. Henkelman, “In vivo detection of applied electric currents by magnetic resonance imaging,” Magnetic Resonance Imaging, vol. 7, no. 1, pp. 89–94, 1989. View at Google Scholar · View at Scopus
  2. M. Eyuboglu, O. Birgul, and Y. Z. Ider, “A dual modality system for high resolution.true conductivity imaging,” in Proceedings of the 11th International Conference on Electrical Bioimpedance (ICEBI '01), pp. 409–413, 2001.
  3. Y. Z. Ider and O. Birgul, “Use of the magnetic field generated by the internal distri- bution of injected currents for Electrical Impedance Tomography (MR-EIT),” Elektrik, vol. 6, pp. 215–225, 1998. View at Google Scholar
  4. H. S. Khang, B. I. Lee, S. H. Oh et al., “J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images,” IEEE Transactions on Medical Imaging, vol. 21, no. 6, pp. 695–702, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. B. I. Lee, S. H. Oh, E. J. Woo et al., “Three-dimensional forward solver and its performance analysis for magnetic resonance electrical impedance tomography (MREIT) using recessed electrodes,” Physics in Medicine and Biology, vol. 48, no. 13, pp. 1971–1986, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. S. H. Oh, B. I. Lee, E. J. Woo et al., “Electrical conductivity images of biological tissue phantoms in MREIT,” Physiological Measurement, vol. 26, no. 2, pp. S279–S288, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Sadleir, S. Grant, S. U. Zhang, S. H. Oh, B. I. Lee, and E. J. Woo, “High field MREIT: setup and tissue phantom imaging at 11 T,” Physiological Measurement, vol. 27, no. 5, pp. S261–S270, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Measurement of nonuniform current density by magnetic resonance,” IEEE Transactions on Medical Imaging, vol. 10, no. 3, pp. 362–374, 1991. View at Publisher · View at Google Scholar · View at Scopus
  9. J. K. Seo, J. R. Yoon, E. J. Woo, and O. Kwon, “Reconstruction of conductivity and current density images using only one component of magnetic field measurements,” IEEE Transactions on Biomedical Engineering, vol. 50, no. 9, pp. 1121–1124, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. E. J. Woo, J. K. Seo, and S. Y. Lee, “Magnetic resonance electrical impedance tomography (MREIT),” in Electrical Impedance Tomography: Methods, History and Applications, D. Holder, Ed., IOP Publishing, Bristol, UK, 2005. View at Google Scholar
  11. M. L. Joy, “MR current density and conductivity imaging: the state of the art,” in Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC '04), pp. 5315–5319, San Francisco, Calif, USA, 2004.
  12. G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Sensitivity of magnetic-resonance current-density imaging,” Journal of Magnetic Resonance, vol. 97, no. 2, pp. 235–254, 1992. View at Google Scholar · View at Scopus
  13. N. Zhang, Electrical impedance tomography based on current density imaging [M.S. thesis], Department of Electrical Engineering, University of Toronto, Toronto, Canada, 1992.
  14. O. I. Kwon, B. I. Lee, H. S. Nam, and C. Park, “Noise analysis and MR pulse sequence optimization in MREIT using an injected current nonlinear encoding (ICNE) method,” Physiological Measurement, vol. 28, no. 11, pp. 1391–1404, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Park, B. I. Lee, O. Kwon, and E. J. Woo, “Measurement of induced magnetic flux density using injection current nonlinear encoding (ICNE) in MREIT,” Physiological Measurement, vol. 28, no. 2, pp. 117–127, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. E. M. Haacke, R. W. Brown, M. R. Thompson, and R. Venkatesan, Magnetic Resonance Imaging: Physical Principles and Sequence Design, John Wiley & Sons, New York, NY, USA, 1999.
  17. R. Kress, Numerical Analysis, vol. 181 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar
  18. W. Gautschi, “On inverses of Vandermonde and confluent Vandermonde matrices,” Numerische Mathematik, vol. 4, pp. 117–123, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. W. Gautschi, “Norm estimates for inverses of Vandermonde matrices,” Numerische Mathematik, vol. 23, pp. 337–347, 1975. View at Google Scholar · View at Zentralblatt MATH